Reaction forces in a Static system need help

1. The problem statement, all variables and given/known data
Rod AB is attached to a collar at A and rests against a roller at C.
a = 107mm,
l = 642mm,
P = 110kN and
Q = 30kN, determine:
The reaction at A (by the vertical rod) (Unit: kN)
The magnitude of the reaction at C (Unit: kN)

2. Relevant equations
This is my first ever post and I’m not sure how to attach an image i have one but it doesn’t have a URL can you just copy and paste images?

For now ill try and explain it in words.
So imagine if you will a smooth vertical rod with a collar that can slide up and down. attached to the collar is a rod(AB) the point where the rod meets the collar is point A and the end of the Rod is point B. The rod goes down and to the right from point A resting midway on a roller point C. The total length of the rod is 642 mm. The roller is 107 mm to the right of the vertical rod that is to say the horizontal distance between point A and point C is 107 mm. At point A there is a force of 30kN down and at point B there is a force of 110kN down

3. The attempt at a solution
The first thing I did was draw a free body diagram it was a diagonal line going from point A down and to the right to point B. I drew the two know forces both down at points A and B. At point A I put a reaction force horizontal to the left and at point C I put a reaction force perpendicular to the rod AB. I then split the reaction at C into horizontal and vertical components. As this system is static the sum of the forces in the x and y direction as well as the sum of the moments is 0 so I calculated that the vertical component of the reaction at C must be 110+30=140kN and that the horizontal component must be equal to the reaction at point A. My problem now is that i can’t solve anything else mainly because i can’t figure out what the angle of the rod is. I have tried calculating the moment around point A and point C both give me equations i can’t solve without the aid of a graphics calculator and even then i get multiple answers. I have been nutting over this for almost a week and i’m starting to think there might not be enough information to resolve it. I know that if i knew the angle of the rod or the point along the rod where C was then i could solve it. please help me.

Attached Images
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